Physics 151 Week 5 Day 1 Topics Area under a velocity graph Constant acceleration equations Pictorial (a.k.a Picture) diagram Solving Motion Problems using Strategic Problem Solving (SPS) Approach

Checking Understanding An arrow is launched vertically upward. It moves straight up to a maximum height, then falls to the ground. The trajectory of the arrow is noted. Which graph best represents the vertical velocity of the arrow as a function of time? Ignore air resistance; the only force acting is gravity. Answer: D Slide 2-28

Answer An arrow is launched vertically upward. It moves straight up to a maximum height, then falls to the ground. The trajectory of the arrow is noted. Which graph best represents the vertical velocity of the arrow as a function of time? Ignore air resistance; the only force acting is gravity. Answer: D Slide 2-29

Velocity to Position: Example 1 Find the position at times t = 1, 2, 3, 4, and 5 seconds. Assume x (t = 0 sec) = 0 m. What is the displacement of the object between t = 1s and t = 3 s? Answer: A Slide 2-34

Velocity to Position: Example 2 Describe in words the motion of the object whose velocity graph is given below. What is happening at t = 2 s? Draw a motion diagram of the objects motion. Draw the corresponding position vs. time graph. Assume initial position is 5 m. Give an example of an object that would move this way Answer: A Slide 2-34

Velocity Graphs to Position Graphs: Watch transitions between motion intervals If vx vs. t graph is continuous, slope of x vs t has no bumps must be smooth (at transition slope from left must = slope from right) Make sure slope of position graph matches velocity graph Example Answer: A Slide 2-34

Start your engine (velocity and acceleration) On the on ramp to Interstate 25 a car accelerates at 7 m/s2 from rest. What is the car's velocity at 1 second after it starts from rest? 2 seconds? 3 seconds? 4 seconds? Express your reasoning in words. Slide 2-34

General Motion Model Graph Relationships Answer: C Slide 2-4

Constant Acceleration Equations Answer: C Area 2 Area 1 Slide 2-4

Constant Acceleration Equations (Equation 3) Answer: C Slide 2-4

Constant Acceleration Equations (Equation 3) Answer: C Unit Check => ??? Slide 2-4

Pictorial Diagrams

Pictorial Diagram Example 1 Answer: C

Pictorial Diagram Example 2 Answer: C

The Sprinter A sprinter accelerates at 2.5 m/s^2 until reaching his top speed of 15 m/s. He then continues to run at top speed. How long does it take him to run the 100 m dash? Answer: C Slide 2-4

Down and Up A ball is released on the left side at a height of 1 m on a frictionless 30 degree slope, |a| = 5 m/s2. At the bottom, it turns smoothly onto a 60 degree slope going back up, |a| = 8.66 m/s2. What maximum height does it reach on the right side? Answer: C Slide 2-4